Forecasts for leverage heterogeneous autoregressive models with jumps and other covariates

• Author: Dong Wan Shin,Ji‐Eun Choi
• Published date: 01 September 2018
• Date: 01 September 2018
• DOI: http://doi.org/10.1002/for.2530

Received: 9 August 2017 Revised: 2 January 2018 Accepted: 12 April 2018

DOI: 10.1002/for.2530

RESEARCH ARTICLE

Forecasts for leverage heterogeneous autoregressive

models with jumps and other covariates

Ji-Eun Choi Dong Wan Shin

Department of Statistics, Ewha University,

Seoul, Korea

Correspondence

Dong Wan Shin, Department of Statistics,

Ewha Womans University,52,

Ewhayeodaegil, Seodaemun-gu, Seoul,

Republic of Korea, 03760.

Email: shindw@ewha.ac.kr

Funding information

National Research Foundation of Korea,

Grant/AwardNumber:

2016R1A2B4008780

Abstract

For leverage heterogeneous autoregressive (LHAR) models with jumps and

other covariates, called LHARX models, multistep forecasts are derived. Some

optimal properties of forecasts in terms of conditional volatilities are discussed,

which tells us to model conditional volatility for return but not for the LHARX

regression error and other covariates. Forecast standard errors are constructed

for which we need to model conditional volatilities both for return and for

LHAR regression error and other blue covariates. The proposed methods are

well illustrated by forecast analysis for the realized volatilities of the US stock

price indexes: the S&P 500, the NASDAQ, the DJIA, and the RUSSELL indexes.

KEYWORDS

asymmetry, implied volatility, jump, LHARX model, realized volatility, volatility index

1INTRODUCTION

The heterogeneous autoregressive (HAR) model of Corsi

(2009) is widely accepted for forecasting volatilities of

financial assets. The model features the long-memory

properties of the volatilities in a conceptually appealing

three-regime autoregression corresponding to day, week,

and month. Following the success of the HAR model,

diverse extensions were made which incorporate leverage

effects related to negative returns, jump components of

continuous-jump decomposition of realized variance, and

implied volatilities (volatility indexes).

There is much evidence for asymmetric volatilities

with respect to returns. Among many others, Campbell

and Hentschel (1992), Bollerslev, Litvinova, and Tauchen

(2006), and Dennis, Mayhew, and Stivers (2006) showed,

and Stivers (2006) showed stronger volatility for nega-

tive returns than for positive returns. The asymmetries, if

properly addressed, improve volatility forecasts,as demon-

strated by Marten, Dijk, and Pooter (2008), Yang and

Chen (2014), and many others. Asymmetric modifica-

tions, called LHAR (leverage heterogeneous autoregres-

sive) models, were developed by McAleer and Medeiros

(2008) and Corsi and Reno (2009). The LHAR model

extends the HAR model of Corsi (2009) by adding lever-

age terms related to negative returns. Leverage models

have also been successful and adopted by many people

for forecasting volatilities; see, among many others, Asai,

McAleer, and Medeiros (2012), Corsi and Reno (2012),

Byun and Kim (2013), Liu and Maheu (2009), Scharth

and Medeiros (2009), Patton and Sheppard (2015), and

Audrino and Knaus (2015).

Other extensions of the HAR model, called HAR-J mod-

els, were made to improve realized volatility forecast by

adding jump components of the realized volatilities by

Andersen, Bollerslev, and Diebold (2007), Corsi, Pirino,

and Reno (2010), Atak and Kapetanios (2013), Yun and

Shin (2015), and many others. Many authors considered

further extensions of the HAR model, among which we

refer to Haugom, Langeland, and Molnar (2014) and Park

and Shin (2014) for models having volatility index; Wen,

Gong, and Cai (2016) and Soucek and Todorova (2014)

for leverage models with jumps; Busch, Christensen, and

Nielsen (2011) for models with jump and volatility index;

and Bekaert and Hoerova (2014) for models having lever-

age, jump, and volatility index.

Journal of Forecasting. 2018;37:691–704. wileyonlinelibrary.com/journal/for © 2018 John Wiley & Sons, Ltd. 691